Two Routers, One NAT

I would like to share this experience and ask one question about one
home network configuration.
I have two routers at home, one provided by the ISP, not wireless,
which I will call router "A"
and another wireless one i recently got for the laptop, I will call it
router "B"
The router A is connected directly to the ISP and there are two
computers connected to the internet through it. And since I can't
connect the router B to the ISP cable directly (their decision) I first
connected the WAN port of router B to one LAN port of router A, which
allowed my laptop to access the internet but i didn't like it that way
because this had to put the laptop behind two NATs.
So i thought of another configuration, to use the router B like a
"wireless HUB only" by connecting one of its LAN ports (instead of the
WAN port) to the router A, which I figured would make the laptop able
to access the ISP's router A directly.
Here came the problem, I noticed that not only the laptop (which is
connected directly to router B) is taking an IP address from the router
B's DHCP, but also the two computers which are connected to the router
A!, and of course this made them all unable to access the internet,
because router B has nothing on the WAN port.
I could solve this problem with one of two methods, either force all
the computers to take IPs from router A, by specifying fixed IPs within
router A's range and use its IP as default gateway, or by completely
disabling the DHCP service on router B, which is a better idea since i
don't need it if i'm using it only like a HUB.
But my question is, what made all the computers including those
connected directly to router A, to connect and take IPs only from the
router B, and on what does it depend that a computer chooses one router
if more than one are on the same network?
(All the computers are running windows XP)